Word problems based on formulation of linear programming, Operation Research

Word problems based on formulation of linear programming problems.

2.   A manufacturer produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine 1 and 3 hours of work on machine 2 to produce a package of nuts. It takes 3 hours on machine 1 and 1 hour on machine 2 to produce a package of bolts. He earns a profit of Rs. 2.50 per package on nuts and Rs. 1 per package on bolts. Form a LPP to maximize his profit, if he operates each machine for almost 12 hours.

script

solution

Let x packages of nuts and y packages of bolts be produced. The objective of the manufacturer to maximize the profit is

Total Time required on machine 1 to produce x packages of nuts and y packages of bolts is equal to

 

Total Time required on the machine 2 to produce x packages of nuts and y packages of bolts is equal to

 s

According to restrictions,

For machine 1

For machine 2

 

Maximize z is equal to

 

Subject to constraints

 

 

To solve this graphically, let us take

The lines are drawn using suitable points on the graph.

The lines intersect at P(3,3)

Now shade the region of intersection of the lines.

The feasible region is OAPB

For the corner point O(0,0), z=

For the corner point A(4,0)

For the corner point P(3,3,)

For the corner point B(0,4)

Clearly z is maximum at x=3 , y=3 and the maximum value is 10.50

 

 

 

 

2.50x + 1y

 

 

1x + 3y

 

 

3x + 1y

 

 

 

 

 

X + 3y ≤ 12

3x + y ≤ 12 and x,y≥0

 

2.50x + y

 

X + 3y ≤ 12

3x + y ≤ 12

X ≥ 0, y ≥ 0

X + 3y =12

3x + y = 12, x=0, y=0

 

 

 

 

 

O(0,0),A(4,0),P(3,3,),B(0,4)

2.5(0) +1(0)=0

2.5(4)+1(0)=10

2.5(3)+1(3)=10.5

2.5(0)+1(4)=4

3.   A shopkeeper deals in 2 items → wall hangings and artificial plants. He had a space to store 80 pieces and Rs. 15000 to invest. A wall hangings cost him Rs. 300 and artificial plant Rs. 150. He can sell a wall hanging at a profit of Rs. 50 and artificial plant at a profit of Rs. 18. Assuming that he can sell all the items that he buys, formulate a LPP in order to maximize his profit.\

script

solution

Let x be the number of wall hangings and y be the number of artificial plants.

Profit of dealer is equal to

Objective function z is equal to

Since dealer invest atmost Rs. 15000

Therefore

Or

Also a dealer has space to store atmost 80 pieces.

Therefore,

 

Maximize z is equal to

Subject to constraints

 

 

 

To solve this graphically, we need to draw the graph

Let us the draw the lines 2x + y ≤100

X + y ≤ 80

X ≥ 0, y ≥ 0

On the graph by using suitable points.

The points of intersection are

Then shade the region of intersection of these two lines

The feasible points are OABC

Now to obtain the maximum value;

For The corner point O(0,0), z=

For the corner point A(50,0)

For the corner point B(20,60)

For the corner point C(0,100)

Clearly we get the maximum value of 2500 at A.(50,0)

 

 

 

50x + 18y

50x + 18y

 

 

300x + 150y ≤ 15000

2x + y ≤ 100

 

 

X + y ≤ 80

X ≥ 0, y ≥ 0

Z = 50x + 18y

2x + y ≤100

X + y ≤ 80

X ≥ 0, y ≥ 0

 

 

 

 

 

 

 

 

 

(20,60)

 

 

O(0,0),A(50,0),B(20,60),(C(0,100)

 

 

 

50(0)+18(0)=0

 

50(50)+18(0)=2500

50(20)+18(60)=2080

50(0)+18(100)=1800

Posted Date: 7/23/2012 4:15:31 AM | Location : United States







Related Discussions:- Word problems based on formulation of linear programming, Assignment Help, Ask Question on Word problems based on formulation of linear programming, Get Answer, Expert's Help, Word problems based on formulation of linear programming Discussions

Write discussion on Word problems based on formulation of linear programming
Your posts are moderated
Related Questions
#A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper

b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y pape

Methods is a tool or a techniques used to collect data. It is procedure for obtaining knowledge based on empirical observation and logical reasoning. Field Study Metho

CLASSIFICATION OF DOCUMENTS  BY PHYSICAL CHARACTERISTICS : Documents of various types have been classified  on the basis of their physical characteristics, familiarity

POLICIES, NORMS AND STANDARDS: Information source; building, an important function of the library, should be based on sound policies and programmes.  The basic question of

QUESTION Discuss the major sources of stress and job burnout and outline the strategies for managing stress. QUESTION How can you use the „Johari Window Model? as a

Merits a.It is simple  to understand  and easy  to calculate. b.It is very  useful  in the  case of data which  are of  qualitative nature  like  intelligence  honesty  be

The plant is using the chase production option and the ATO process design. The BOM is illustrated below.   Requirement The factory works on a process layout but

A series of questionnaire for Delphi were mailed to the selected experts who meet the criteria that mention in above. The overall purpose of the Delphi technique was to achieve the

one example